Markov chains satisfying simple drift conditions for subgeometric ergodicity

Markov chains satisfying simple drift conditions for subgeometric ergodicity

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Article ID: iaor20021368
Country: United States
Volume: 17
Issue: 2
Start Page Number: 109
End Page Number: 120
Publication Date: Jan 2001
Journal: Communications in Statistics - Stochastic Models
Authors:
Keywords: stochastic processes
Abstract:

This paper is concerned with ergodic Markov chains satisfying a sequence of drift conditions that imply (f, r)-regularity of the chain, by which subgeometric ergodicity is ensured. An interesting exact trade-off result between the exponents of f and r for a special class of state space models by Tuominen and Tweedie is extended here from integers to real numbers for general Markov chains satisfying these drift conditions simultaneously as well as standard requirements for ergodic Markov chains. In Section 3, we will illustrate by the state space models that the utilization of these drift conditions is a very convenient way to show subgeometric ergodicity of Markov chains including the exact trade-off between the exponents of f and r.

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